Theorem 3.1 (Auslander and Lichtenbaum [1]}, [2]})
Let \(R\)  be a regular local ring and let \(M, N\in \operatorname{mod}(R)\) . If \(M\otimes _RN\)  is nonzero and torsion-free, then \(M\)  and \(N\)  are torsion-free and Tor-independent.

